Question.5644 - You are a data analyst for FreshMart Groceries, a small supermarket focusing on fresh produce and daily essentials. The store has observed increasing customer traffic and needs your expertise to improve inventory management, pricing strategies, and quality control. Your task is to analyze data to help FreshMart optimize its operations. FreshMart sells various items in its store, including snacks, drinks, and fresh bakery products. Each category contributes significantly to its revenue. However, managing inventory and ensuring quality under variable customer demand is challenging. You will use probability and statistical tools to provide actionable insights. Question 1: Validating a Discrete Probability Distribution: FreshMart tracks the purchase probabilities of four popular snack types based on historical sales data: Chips: P(Chips) = 0.35 Cookies: P(Cookies) = 0.30 Nuts: P(Nuts) = 0.20 Crackers: P(Crackers) = 0.15 Based on the above data, verify that the given probabilities form a valid discrete probability distribution and explain what it means if the probabilities do not sum to 1. Question 2: Computing Expected Values : FreshMart sells fresh juice in three sizes, with the following prices and customer purchase probabilities: Small Juice: $3.50 (P(Small)=0.4) Medium Juice: $5.00 (P (Medium)=0.35) Large Juice: $7.00 (P(Large)=0.25) Based on the above data, calculate the expected value (average revenue) and standard deviation per juice purchase. Question 3: Applying the Binomial Distribution: FreshMart's bakery division produces a line of bread with a 90% success rate for quality control. To ensure consistent quality, the bakery independently tests a random sample of 12 loaves. Based on the context, answer the following: Calculate the probability that exactly 10 out of the 12 tested loaves meet the quality standard. Calculate the probability that at least 8 out of 10 loaves meet the quality standard.
Answer Below:
Question 10.35 + 0.30 + 0.20 + 0.15 = 1 The probability sums to 1 and each probability is between 0 and 1. Therefore, this is a valid discrete probabi...
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